injector pic 16f
Even a half bridge is not the ultimate one for your application.
Leave this 'bridge' concept.,if you really like that,change your project title to 'motor controlling'
on way is to use a triac for switching the relay.And control the triggering angle of the triac with the microcontroller.Insert a current transformer in tha path which fill give you a feedback of how much current is flowing,and transfer that data to the microcontroller again so that you have a control over the current.
hope you hav not gotten any clear picture.
but wait,whats the relay going to be tested.make? part number? type? do you have one in hand?
Only by looking into its characteristics and specifications,you can start designing/choosing the circuit.